Signed graph (original) (raw)
En teoría de grafos, un grafo signado o grafo con signos es un grafo cuyas aristas tienen un signo positivo o negativo, que puede representar cualquier relación dicotómica. Estos grafos cumplen con la propiedad de dualidad antitética, de modo que el dual de un grafo signado implica cambiar el signo de sus aristas. Además, el dual del dual de un grafo signado, vuelve a restablecer las aristas a sus signos originales.
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| dbo:abstract | En teoría de grafos, un grafo signado o grafo con signos es un grafo cuyas aristas tienen un signo positivo o negativo, que puede representar cualquier relación dicotómica. Estos grafos cumplen con la propiedad de dualidad antitética, de modo que el dual de un grafo signado implica cambiar el signo de sus aristas. Además, el dual del dual de un grafo signado, vuelve a restablecer las aristas a sus signos originales. (es) In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering. (en) 그래프 이론에서 부호형 그래프(signed graph)란 각 변(edge)이 양부호나 음부호를 가지는 그래프를 의미한다. (ko) |
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| rdfs:comment | En teoría de grafos, un grafo signado o grafo con signos es un grafo cuyas aristas tienen un signo positivo o negativo, que puede representar cualquier relación dicotómica. Estos grafos cumplen con la propiedad de dualidad antitética, de modo que el dual de un grafo signado implica cambiar el signo de sus aristas. Además, el dual del dual de un grafo signado, vuelve a restablecer las aristas a sus signos originales. (es) 그래프 이론에서 부호형 그래프(signed graph)란 각 변(edge)이 양부호나 음부호를 가지는 그래프를 의미한다. (ko) In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. (en) |
| rdfs:label | Grafo signado (es) 부호형 그래프 (ko) Signed graph (en) |
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